# Transformation of optimal control problems of descriptor systems into problems with state-space systems

Jovan Stefanovski

# Abstract:

We show how we can transform the ${\mathscr H}_\infty$ and ${\mathscr H}_2$ control problems of descriptor systems with invariant zeros on the extended imaginary into problems with state-space systems without such zeros. Then we present necessary and sufficient conditions for existence of solutions of the original problems. Numerical algorithm for ${\mathscr H}_\infty$ control is given, based on the Nevanlinna-Pick theorem. Also, we present an explicit formula for the optimal ${\mathscr H}_2$ controller.

# Keywords:

parametrization of stabilizing controllers, inner matrices, ${\mathscr H}_\infty$ and ${\mathscr H}_2$ control

93D15, 49J15

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